The present invention relates to a computerized method for simulating deformation of rubber compound comprising a rubber component, silica particles and an interfacial coupling agent, more particularly to a method for generating a finite element model of the rubber compound capable of accurately simulating the deformation.
Conventionally, rubber compounds used in various industrial products, e.g. tires, sports goods and the like contain carbon black as a reinforcing filler to improve mechanical characteristics.
In recent years, on the other hand, silica becomes widely used instead of carbon black for the following reasons. Generally, an energy loss in a silica-rich compound is less in comparison with a carbon-rich compound, therefore, by using a silica-rich compound as the tread rubber of a tire, the rolling resistance can be decreased which contributes to lessen the fuel consumption of the vehicle. Further, silica is a non-petroleum resource, therefore to use silica as reinforcing fillers is environmentally-friendly.
Thus, in view of research and development of vehicle tires, it is very beneficial to accurately simulate deformations of a rubber compound containing silica as reinforcing filler particles.
Computerized methods for simulating deformation of rubber compound are disclosed in Japanese patent No. 3668238 and the following non-patent document.
“A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials” Authors: Ellen M. Arruda and Marry C. Boyce, Publication: Journal of the Mechanics and Physics of Solids, vol. 41, issue 2, Pages 389-412, Publication Date February 1993
In Japanese patent No. 3668238, the finite element model of a rubber compound includes a rubber component model and a filler particle model, and by the use of a finite element method, a deformation calculation is made taking account of influence of the filler.
Therefore, in the case of a silica-rich rubber compound, used is a rubber compound model including a rubber component model and silica particle models. And in order to make a deformation calculation, on the silica particle models, physical properties, e.g. elastic modulus as a hard elastic body are defined. On the rubber component model, physical properties, e.g. relationship between stress and elongation as a viscoelastic body is defined.
However, if a deformation simulation is made by applying strain e.g. tensile deformation to such rubber compound model, simulation results are not always coincide with actual phenomena although in the case of a carbon-rich rubber compound simulation results are well coincide with actual phenomena.
Therefore, the present inventors studied the differences between simulation results and actual phenomena and found that such difference is caused by an interfacial coupling agent added in a silica-rich rubber compound.